TY - JOUR

T1 - Walking around fat obstacles

AU - Chew, L. Paul

AU - David, Haggai

AU - Katz, Matthew J.

AU - Kedem, Klara

N1 - Funding Information:
2M. Katz and K. Kedem were supported in part by a grant from the Israel Science Foundation. K. Kedem was also supported by the Mary Upson Award from the College of Engineering at Cornell University, and by a grant from the US–Israeli Binational Science Foundation.
Funding Information:
1L.P. Chew was supported in part by the National Science Foundation (EIA-9726388), by DARPA through ONR (N00014-96-1-0699), and by a grant from the US–Israeli Binational Science Foundation.

PY - 2002/8/16

Y1 - 2002/8/16

N2 - We prove that if an object O is convex and fat then, for any two points a and b on its boundary, there exists a path on O's boundary, from a to b, whose length is bounded by the length of the line segment ab times some constant β. This constant is a function of the dimension d and the fatness parameter. We prove bounds for β, and show how to efficiently find paths on the boundary of O whose lengths are within these bounds. As an application of this result, we briefly consider the problem of efficiently computing short paths in ℝd in the presence of disjoint convex fat obstacles.

AB - We prove that if an object O is convex and fat then, for any two points a and b on its boundary, there exists a path on O's boundary, from a to b, whose length is bounded by the length of the line segment ab times some constant β. This constant is a function of the dimension d and the fatness parameter. We prove bounds for β, and show how to efficiently find paths on the boundary of O whose lengths are within these bounds. As an application of this result, we briefly consider the problem of efficiently computing short paths in ℝd in the presence of disjoint convex fat obstacles.

KW - Computational geometry

KW - Fat objects

KW - Short paths

UR - http://www.scopus.com/inward/record.url?scp=0037119070&partnerID=8YFLogxK

U2 - 10.1016/S0020-0190(01)00321-0

DO - 10.1016/S0020-0190(01)00321-0

M3 - Article

AN - SCOPUS:0037119070

VL - 83

SP - 135

EP - 140

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 3

ER -